Nuclear magnetic resonance (NMR) spectroscopy is a spectroscopic technique to observe local magnetic fields around atomic nuclei. A sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio frequency (RF) pulses into nuclear magnetic resonance, which is detected with sensitive RF receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. For example, NMR spectroscopy is used to identify monomolecular organic compounds, proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. Common types of NMR include proton and carbon-13 NMR spectroscopy, just to name a few examples.
Upon excitation of the sample with a radio frequency (typically 60-1000 MHz) pulse, a nuclear magnetic resonance response is obtained which is referred to as free induction decay (FID) herein. The FID is typically a weak signal and may require sensitive RF receivers to detect such signals. A Fourier transform can be applied to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID typically has a low signal-to-noise ratio. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions whereas they can be very long in gases.
Some existing NMR signal detection methods are based on computing the derivation of the frequency spectrum in a first step. As a consequence, broad signals (i.e., signals extending over a relatively large frequency interval in the frequency domain) get lost, whereas narrow signals are preserved. Further the derivation generates artefacts which can lead to false positives and false negatives. Such disadvantages can be partially remedied with the Continuous Wavelet Transformation, for example.